Robots are automated devices able to manipulate objects using a series of links, which in turn are interconnected via one or more robotic joints. Each joint in a typical robot represents at least one independent control variable, i.e., a degree of freedom (DOF). End-effectors such as hands, fingers, or thumbs are ultimately actuated to perform a task at hand, e.g., grasping a work tool or an object. Therefore, precise motion control of the robot may be organized by the level of task specification, including object, end-effector and joint-level control. Collectively, the various control levels achieve the required robotic mobility, dexterity, and work task-related functionality.
Tendon transmission systems are often used in robotic systems, e.g., in the actuation of robotic fingers in high degree of freedom (DOF) hands. For force control of a given tendon-driven finger, the desired torques on the finger must be translated into tension on the tendons. Since tendons can only transmit forces in tension, i.e., in a pull-pull arrangement, the number of tendons and the number of actuators must exceed the DOF to achieve fully determined control of the tendon-driven finger. To become fully determined, the finger needs only one tendon more than the number of DOF, which is known as an n+1 arrangement.
Given a desired set of joint torques, an infinite set of solutions exist for corresponding tendon tensions. Any solution, however, that assigns a negative tension value to a tendon is not physically valid. This is due to the unidirectional nature of the tendons, i.e., tendons can resist extension but not compression. Existing methods for this problem provide solutions that ensure that all tendon tensions are greater than or equal to zero. However, when upper saturation limits are achieved, e.g., when the maximum tension limit of the hardware is met, the resulting joint torques may become unpredictable, and undesired coupling may be introduced.